On 2013-10-06 00:50, rwg wrote:

On 2013-10-05 23:40, Adam P. Goucher wrote:

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Bill wrote:

OMG, there really ARE 13 of them little goobers? gosper.org/flake13.png

That's not so boring.

I don't think so, unfortunately, if you're just rotating that portion of the Cl(flowsnake)\Int(Cl(flowsnake)) -- according to my calculations, the complex number solution has a modulus slightly different from 1 (so you'll need to rotate and enlarge).

Can you zoom further into the centre of the design to check whether the correspondence is exact? Will do. Meanwhile, note http://gosper.org/flake13a.png . I didn't compute that arctan(7 √3/11). I just stumbled on it and it looked right. But not exactly, I agree. --rwg

On zooming, 7/11 is definitely wrong. If there is a solution, it's closer to 16/25. But as I slide past the optimum, the line segments never quite superpose. When they're collinear, they slightly overhang. When not overhung, they're off by about a line thickness. Aargh, my initial doubt seems vindicated. How cruel and unusual. --rwg

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Nevertheless, I can confirm that the second frame does work (but the

angle

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is not 7pi/33).

Sincerely,

Adam P. Goucher

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On Fri, Oct 4, 2013 at 10:06 PM, Bill Gosper <billgosper@gmail.com> wrote:

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On Fri, Oct 4, 2013 at 9:52 PM, Bill Gosper <billgosper@gmail.com> wrote:

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(Easy for YOU to say.) gosper.org/flakes.png First frame is swing angle π/3, confirming DanA's guess about trisected areas. 2nd frame is implausible swing angle 7π/33, or VERY nearly, showing subflake at a peculiar angle. 3rd frame is even weirder angle that seems to make a triskelion out of ten tiny flakes. Doubt this one.

Especially since they number thirteen.

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--rwg